Problem: Evaluate. $(-7)^{^{\scriptsize\dfrac53}}\cdot\left(\dfrac{1}{56}\right)^{^{\scriptsize\dfrac53}}=$
$\begin{aligned} (-7)^{^{\scriptsize\dfrac53}}\cdot\left(\dfrac{1}{56}\right)^{^{\scriptsize\dfrac53}}&=\left(-\dfrac{7}{56}\right)^{^{\scriptsize\dfrac53}} \\\\ &=\left(-\dfrac{1}{8}\right)^{^{\scriptsize\dfrac53}} \\\\ &=\dfrac{1}{(-8)^{^{\scriptsize\dfrac53}}} \\\\ &=\dfrac{1}{\left(\sqrt[3]{-8}\right)^5} \\\\ &=\dfrac{1}{(-2)^5} \\\\ &=-\dfrac{1}{32} \end{aligned}$ In conclusion, $(-7)^{^{\scriptsize\dfrac53}}\cdot\left(\dfrac{1}{56}\right)^{^{\scriptsize\dfrac53}}=-\dfrac{1}{32}$